On 7 Dec 2008, at 04:30, George Pollard wrote:
This is a little bit random, but I was just wondering if anyone knew where the $ low-precedence parenthesis-eliminating application operator originated. The Haskell Report doesn't mention anything, and I can't search for "$" on Google. So... who thought it up? Does it originate in an earlier language, or is it uniquely Haskellish? :)
As for the operator itself, it appears in Alonzo Church, "The Calculi of Lambda-Conversion", where it is written as exponentiation, like x^f, or typographically as f x One can define operators a ^ b := b(a) -- Application in inverse. (a * b)(x) := b(a(x)) -- Function composition in inverse. (a + b)(x) := a(x) * b(x) O(x) := I -- Constant function returning identity. I(x) := x -- Identity. and use them to define lambda calculus (suffices with the first four; Church reverses the order of "*"). Then on Church's natural number functionals, these are just the expected natural number operations. Hans